Topological data analysis (TDA) is a relatively new area of computational mathematics that quantifies the shape of data by computing topological properties of the data. There are various approaches of topological inference, e.g., level sets or mode clusters [1]}. The most prominent algorithm in TDA is persistent homology [2]}, [3]}. PH takes in data and a metric, and outputs topological features (e.g., connected components and loops) and their persistence across different scales of the data. The computation crucially depends on the choice of filtration, which is a nested sequence of spaces built on the data, that is indexed by a scale parameter [3]}, [5]}.
There are many software for persistent homology [6]}; however, the software used is often selected based on the types of filtrations available within it. The choice of filtration for applications is an active area of research, and there is no one-size-fits-all filtration for biological applications [7]}. The persistence of the topological features as well as where topological features appear and die in the filtration may provide insight into biological processes and models.
